Binder-free and self-standing carbon nanotube (CNT) electrodes of tens of microns in thickness have been assembled via a vacuum-filtration process of oxidized few-walled CNTs (FWNTs), with different amounts of oxygen functional groups on FWNTs. Sub-millimetre long FWNTs can provide high electrical conductivity and mechanical strength in self-standing porous networks by reducing the number of junctions among FWNTs. We show that the gravimetric capacity of FWNT electrodes in lithium cells can be enhanced by increasing oxygen functional groups on FWNTs, which results from Faradaic reactions between lithium ions and surface oxygen functional groups. These self-standing FWNT electrodes (free of binder/additive and current collector) can provide a high gravimetric energy of 200 W h kg−1 at a high power of 10 kW kg−1, showing promise as the positive electrode for light-weight, high-power lithium batteries.